Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.physa.2020.124731

arXiv

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DOI： 10.1140/epjb/e2020-10264-5

arXiv

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1140/epjb/e2019-100269-8

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Other Link： http://link.springer.com/article/10.1140/epjb/e2019-100269-8/fulltext.html

Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.physa.2019.121395

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1140/epjb/e2018-90426-8

arXiv

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1140/epjb/e2018-80707-7

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1140/epjb/e2017-80286-1

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Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.nuclphysb.2016.12.024

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Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.71.2.0_2641

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Language：English   Publisher：ELSEVIER SCIENCE BV  

The overlap (inner product) between the ground-state eigenvectors with proximate interaction parameters, the so-called fidelity, plays a significant role in the quantum-information theory. In this paper, the critical behavior of the fidelity susceptibility is investigated for a two-dimensional transverse-field (quantum) Ising model by means of the numerical diagonalization method. In order to treat a variety of system sizes N = 12, 14, ... , 32, we adopt the screw-boundary condition. Finite-size artifacts (scaling corrections) of the fidelity susceptibility appear to be suppressed, as compared to those of the Binder parameter. As a result, we estimate the fidelity susceptibility critical exponent as alpha(F) = 0.715(20). (C) 2013 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physa.2013.05.024

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The criticality of the (2+1) -dimensional XY model is investigated with the numerical diagonalization method. So far, it has been considered that the diagonalization method would not be very suitable for analyzing the criticality in large dimensions (d≥3)
in fact, the tractable system size with the diagonalization method is severely restricted. In this paper, we employ Novotny's method, which enables us to treat a variety of system sizes N=6,8,...,20 (N is the number of spins constituting a cluster). For that purpose, we develop an off-diagonal version of Novotny's method to adopt the off-diagonal (quantum-mechanical XY) interaction. Moreover, in order to improve the finite-size-scaling behavior, we tune the coupling-constant parameters to a scale-invariant point. As a result, we estimate the critical indices as ν=0.675 (20) and γν=1.97 (10). © 2008 The American Physical Society.

DOI： 10.1103/PhysRevE.78.021135

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Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as ν=0.6245 (28) and yh =2.4709 (73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely. © 2006 The American Physical Society.

DOI： 10.1103/PhysRevE.74.016120

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DOI： 10.1103/PhysRevE.73.016114

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DOI： 10.1103/PhysRevE.72.036104

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DOI： 10.1103/PhysRevE.71.046112

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Language：English   Publisher：PHYSICAL SOC JAPAN  

Synchrotron X-ray diffraction measurements on a spin-Peierls material CuGeO3 in applied magnetic fields, H, up to 15 T are made. We find that the temperature, T, dependence of the incommensurate Bragg peak at a lower H is quite different from that at a higher H. At sufficiently high fields, we find that the lattice incommensurability, deltal, is almost independent of T, while at H slightly above the critical field = 12.25 T for the commensurate to incommensurate transition, deltal decreases with increasing T. We interpret that this finding is due to a stabilization of the incommensurate state by a strong magnetic field which suppresses thermal fluctuations.

DOI： 10.1143/JPSJ.73.2650

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A three-dimensional Ising model was numerically investigated with the plaquette interactions. It was found that the interfacial energy lacks the surface tension term and thermally activated undulations must be promoted significantly because of the absence of the surface tension. It was noticed that a phase transition occurs at a considerably low temperature quite reminiscent of that of the two-dimensional Ising model. It was also confirmed that the phase transition belongs to the three-dimensional Ising university class.

DOI： 10.1103/PhysRevE.70.026120

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The three-dimensional discrete folding by means of the density-matrix renormalization group was investigated. The technique was found to be successful even in the problem of soft materials such as fluid membranes. The bulk properties of discrete folding was investigated in detail taking the advantage that the technique can allow to treat very large system sizes. The folding entropy which appears to lie within the best analytical bound obtained through combinatorics arguments was also calculated.

DOI： 10.1103/PhysRevE.70.016101

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Language：English   Publisher：ELSEVIER SCIENCE BV  

We study the emptiness formation probability (EFP) for the spin 1/2 XXZ spin chain. EFP P(n) detects a formation of ferromagnetic string of the length n in the ground state. It is expected that EFP decays in a Gaussian way for large strings P(n) similar to n(-gamma) C-n<^>2. Here, we propose the explicit expressions for the rate of Gaussian decay C as well as for the exponent gamma. In order to confirm the validity of our formulas, we employed an ab initio simulation technique of the density-matrix renormalization group to simulate XXZ spin chain of sufficient length. Furthermore, we performed Monte Carlo integration of the Jimbo-Miwa multiple integral for P (n). Those numerical results for P (n) support our formulas fairly definitely. (C) 2003 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0375-9601(03)00616-9

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Language：English   Publisher：AMER PHYSICAL SOC  

We exactly evaluate the third-neighbor correlator <S(j)(z)S(j+3)(z)> and all the possible nonzero correlators <S(j)(alpha)S(j+1)(beta)S(j+2)(gamma)S(j+3)(delta)> of the one-dimensional spin-1/2 Heisenberg XXX antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln 2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.

DOI： 10.1103/PhysRevE.67.065101

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DOI： 10.1103/PhysRevE.68.031901

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DOI： 10.1103/PhysRevE.68.031901

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Language：Japanese   Publisher：物性研究刊行会  

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Other Link： http://hdl.handle.net/2433/97431

Language：English   Publisher：AMERICAN PHYSICAL SOC  

An elastic string embedded between rigid walls is simulated by means of the density-matrix renormalization group. The string collides against the walls owing to the quantum-mechanical zero-point fluctuations. Such a "quantum entropic" interaction has come under thorough theoretical investigation in the context of the stripe phase observed experimentally in doped cuprates. We found that the excitation gap opens in the form of an exponential singularity DeltaEsimilar toexp(-Ad(sigma)) (d=wall spacing) with the exponent sigma=0.6(3), which is substantially smaller than the mean-field value sigma=2. That is, the excitation gap is much larger than that anticipated from mean field, suggesting that the string is subjected to a robust pinning potential due to the quantum collisions. This feature supports Zaanen's "order out of disorder" mechanism, which would be responsible for the stabilization of the stripe phase.

DOI： 10.1103/PhysRevB.66.184501

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Language：English   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

Quantum S = 1 spin chain with single-ion anisotropy in the presence of an external magnetic field is investigated by means of the finite-temperature density-matrix renormalization group. Emphasis is laid on the point that the underlying physics differs significantly with respect to magnetic-field directions. There appear various phases, which are absent in the classical counterpart studied extensively in the past. We argue possible implications of our numerical results in the field-induced magnetic long-range ordering observed experimentally in NDMAP. (C) 2002 Elsevier Science Ltd. All rights reserved.

DOI： 10.1016/S0022-3697(02)00140-3

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We study the spin-1/2 Heisenberg XXX antiferromagnet for which the spectrum of the Hamiltonian was found by Bethe in 1931. We study the probability of the formation of ferromagnetic string in the antiferromagnetic ground state, which we call emptiness formation probability P(n). This is the most fundamental correlation function. We prove that, for short strings, it can be expressed in terms of the Riemann zeta function with odd arguments, logarithm In 2 and rational coefficients. This adds yet another link between statistical mechanics and number theory. We have obtained an analytical formula for P(5) for the first time. We have also calculated P(n) numerically by the density matrix renormalization group. The results agree quite well with the analytical results. Furthermore, we study the asymptotic behaviour of P (n) at finite temperature by quantum Monte Carlo simulation. This also agrees with our previous analytical results.

DOI： 10.1088/0305-4470/35/20/305

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量子XXZスピン鎖は厳密に解けることはよく知られているが、相関関数を計算することは、特別な場合(XX0スピン鎖)を除いて依然として困難な問題である.ただし、よく知られているように、絶対零度でmasslessの臨界領域では共形場の理論を援用することによって非常に遠方の二点相関関数の漸近形の情報を引き出すことはできる。ところが、最近、Emptiness Formation Probability (EFP)とよばれる、ある長さnにわたってスピンの縦成分が強磁性的になる確率P(n)について様々な発展が報告されている。これは今まであまり考察されてこなかった新しい相関関数であり、元来はより物理的な相関関数を厳密に計算するためのファーストステップとして導入されたものである。しかし、最近ではP(n)それ自体、多くの興味深い性質を持つことが認識されつつある.特に、臨界領域では通常の二点相関関数は絶対零度で代数的に減衰するのに対して、P(n)はガウシアン的に減衰すると議論されている.また、有限温度ではP(n)は指数的に減衰し、その"相関距離"は1サイト当たりの自由エネルギーで表わされると考えられている。本レビューでは、現在までのXXZスピン鎖のEFPに関連する発展をまとめた後、その特別な場合であるXX0スピン鎖で、P(n)を厳密に計算し、上の漸近予想が正しいことを示す.また、XXXスピン鎖やXXZスピン鎖の特別な場合(Δ=1/2)で最近、報告されている解析的な結果について紹介する。また、同時に、絶対零度では密度行列繰り込み群を、有限温度では連続時間量子モンテカルロを用いてP(n)を直接数値的に評価して、上記の漸近形の予想が肯定的に支持されることをみた。

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Other Link： http://dl.ndl.go.jp/info:ndljp/pid/10940151

Language：English   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

Critical properties of field-induced magnetic phases are investigated in the one-dimensional S = 1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.

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Recently, there arose a problem of 'quantum string,' which is a linelike object meandering quantum-mechanically and undergoes entropy-reducing collisions with adjacent neighbors. In this paper, we overview underlying physics of the quantum string, and report our simulation result on the collision-induced entropy loss of a quantum string between walls by means of the density-matrix renormalization group.

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Strong-coupling expansion is performed for the lattice phi(4) model in 1 + 1 dimensions. Because the strong-coupling limit itself is not solvable, we employed numerical calculations so as to set up unperturbed eigensystems. Restricting the number of Hilbert-space bases, we performed linked-cluster expansion up to 11th order. We carried out an alternative simulation by means of the density-matrix renormalization group. Thereby, we confirmed that our series-expansion data with a convergence-acceleration trick are in good agreement with the simulation result. Through the analytic continuation to the domain of negative biquadratic interaction, we obtain the false-vacuum decay rate. Contrary to common belief that the tunnelling phenomenon lies out of perturbative treatments, our series expansion reproduces the instanton-theory behaviour for a high potential barrier. For a shallow barrier, in contrast, our result tells us that the relaxation is no longer described by an instanton, but the decay rate acquires notable enhancement.

DOI： 10.1088/0305-4470/34/50/304

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We study a correlation function for the one-dimensional isotropic Xy model (XXO model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.

DOI： 10.1143/JPSJ.70.3535

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Nonequilibrium electron transport through the Kondo impurity is investigated numerically for the system with 20 conduction-electron levels. The electron current under finite voltage drop is calculated in terms of the `conductance viewed as transmission' picture proposed by Landauer. Here, we take into account the full transmission processes of both the many-body correlation and the hybridization amplitude up to infinite order. Our results demonstrate, for instance, how the exact solution of the differential conductance by Schiller and Hershfield obtained at the Toulouse point becomes deformed by more realistic interactions. The differential-conductance-peak height is suppressed below e(2)/h with the width hardly changed through reducing the Kondo coupling from the Toulouse point, whereas it is kept unchanged by further increase of the coupling. We calculated the nonequilibrium local Green function as well. This clarifies the spectral property of the Kondo impurity driven far from equilibrium. (C) 2001 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S1386-9477(01)00173-4

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Language：English   Publisher：AMER PHYSICAL SOC  

A quantum string, which was brought into discussion recently as a model for the stripe phase in doped cuprates, is simulated by means of the density-matrix-renormalization-group method. String collides with adjacent neighbors, as it wanders, owing to quantum zero-point fluctuations. The energy cost due to the collisions is our main concern. Embedding a quantum string between rigid walls with separation d, we found that for sufficiently large d, collision-induced energy cost obeys the formula similar to exp(-Ad(alpha)) with alpha =0.808(1), and the, string's mean fluctuation width grows logarithmically similar to log d. Those results are not understood in terms of a conventional picture that the string is "disordered," and only short-wavelength fluctuations contribute to collisions. Rather, our results support a recent proposal that owing to collisions, short-wavelength fluctuations are suppressed, but instead, long-wavelength fluctuations become significant. This mechanism would be responsible for stabilizing the stripe phase.

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Ground state of the two-dimensional hard-core-boson model subjected to external magnetic field and quenched random chemical potential is studied numerically. In experiments, magnetic-field-tuned superconductor-insulator transition has already come under through investigation, whereas in computer simulation, only randomness-driven localization (with zero magnetic field) has been studied so far: The external magnetic field brings about a difficulty that the hopping amplitude becomes complex number (through the gauge twist), for which the quantum Monte-Carlo simulation fails. Here, we employ the exact diagonalization method, with which we demonstrate that the model does exhibit field-tuned localization transition at a certain critical magnetic field. At the critical point, we found that the DC conductivity is not universal, but is substantially larger than that of the randomness-driven localization transition at zero magnetic field. Our result supports recent experiment by Markovic et al. reporting an increase of the critical conductivity with magnetic field strengthened. (C) 2001 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0921-4534(00)01741-X

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Detailed results of heat capacity and magnetization measurements are reported on a single crystal sample of the spin S=1 quasi-one-dimensional Heisenbrrg antiferromagnet Ni(C5H14N2)(2)N-3(PF6), abbreviated NDMAP. From these results, we constructed the magnetic field (H) versus temperature phase diagram of this compound which exhibits the quantum disordered Haldane, field-induced long-range-ordered (LRO) and thermally disordered paramagnetic phases. The phase boundary curve separating the paramagnetic and LRO phases is anisotropic; the increase of the Neel temperature (T-N) with H along the a and b axes is more rapid than that along the c axis. We calculated T-N as a function of H by taking into account the interchain coupling as the form of a mean held. The calculation of the staggered susceptibility of the S=1 one-dimensional antiferromagnet with an easy-plane anisotropy shows quite different behavior in the different field directions, resulting in the anisotropic phase boundary curve. A good agreement is obtained between theory and experiment using the exchange and anisotropy constants obtained from the neutron scattering experiment.

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Chiral order of the Josephson-junction ladder with half a flux quantum per plaquette is studied by means of the exact diagonalization method. We consider an extreme quantum limit where each superconductor grain (order parameter) is represented by S = 1/2 spin. So far, the semi-classical S -> infinity case, where each spin reduces to a plane rotator: has been considered extensively. We found that in the case of S = 1/2, owing to the strong quantum fluctuations, the chiral (vortex lattice) order becomes dissolved except in a region, where attractive intrachain and, to our surprise, repulsive interchain interactions both exist. On the contrary, for considerably wide range of parameters, the superconductor (XY) order is kept critical. The present results are regarded as a demonstration of the critical phase accompanying chiral-symmetry breaking predicted for frustrated XXZ chain field-theoretically.

DOI： 10.1007/s100510070144

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Electron gas in a wire connected to two terminals with potential drop is studied with the Schwinger-Keldysh formalism. Recent studies, where the current is enforced to flow with a Lagrange-multiplier term, demonstrated that the current enhances the one-particle-correlation function. We report that in our model, such enhancement is not guaranteed to occur, but conditional both on the potential drop and the positions where we observe the correlation function. That is, under a certain condition, spatially modulated pattern is formed in the wire owing to the nonequilibrium current. (C) 2000 Published by Elsevier Science B.V.

DOI： 10.1016/S0375-9601(00)00543-0

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The systematic trend of spin correlation in the S = 1/2 quantum antiferromagnetic chain with the next nearest neighbor exchange interaction, which competes with the alternating nearest neighbor interaction, is studied at zero temperature as well as at finite temperatures, focusing our attention on their incommensurate nature. We find that, at zero temperature, the dynamical structure factor exhibits a minimal gap at a commensurate or at an incommensurate wave number, which is explained as a consequence of a domain-wall like excitation due to the structure of the dimer order. At finite temperatures, the static structure factor is shown to exhibit a peak at a commensurate or at an incommensurate wave number, depending on thr temperature. The boundary between them, called the Lifshitz temperature, is determined. The behavior is discussed in connection with the experimental aspect of the recent neutron inelastic scattering in CuGeO3.

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Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming reservoir Hilbert space to being tractable in computers. Both the implementation of the algorithm and the precision are reported in detail. We evaluate the dynamical susceptibility (resolvent) with the continued-fraction-expansion formula. Through analysing the resolvent over a frequency range, which is often called "interesting" frequency, we obtain the damping rate and the oscillation frequency. Our results agree with those of a recent quantum Monte-Carlo study, which concludes that the critical dissipation from oscillatory to over-damped behavior decreases as the tunneling amplitude is strengthened.

DOI： 10.1007/s100510051037

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Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated by means of the exact-diagonalization method for the system sizes up to L = 5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate, with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as nu = 2.3 +/- 0.6 and z = 2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical response function) is expressed in terms of the continued-fraction form consisting of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as sigma(c)(omega --> 0) = 0.135 +/- 0.01((2e)(2)/h).

DOI： 10.1007/s100510050759

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